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arXiv · 2412.13160

Quantum community detection via deterministic elimination

Chukwudubem Umeano·Stefano Scali·Oleksandr Kyriienko
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Abstract

We propose a quantum algorithm for calculating the structural properties of complex networks and graphs. The corresponding protocol -- deteQt -- is designed to perform large-scale community and botnet detection, where a specific subgraph of a larger graph is identified based on its properties. We construct a workflow relying on ground state preparation of the network modularity matrix or graph Laplacian. The corresponding maximum modularity vector is encoded into a $\log(N)$-qubit register that contains community information. We develop a strategy for ``signing'' this vector via quantum signal processing, such that it closely resembles a hypergraph state, and project it onto a suitable linear combination of such states to detect botnets. As part of the workflow, and of potential independent interest, we present a readout technique that allows filtering out the incorrect solutions deterministically. This can reduce the scaling for the number of samples from exponential to polynomial. The approach serves as a building block for graph analysis with quantum speed up and enables the cybersecurity of large-scale networks.

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Chukwudubem Umeano, Stefano Scali, Oleksandr Kyriienko. 2024-12-17. Quantum community detection via deterministic elimination. https://doi.org/10.1103/s7cm-c9qy

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